Monthly Archives: May 2016

Vocational Ed: Advancing the Debate

(note: I’m calling it vocational ed in the title, but throughout will use career/tech, career ed, whatever.)

In my last post I discussed the reason that skilled career/vocational education training has declined–which is not because schools themselves sneer at anything less than college. For those who keep griping about the “disdain” America shows “the trades”, I hope the last essay provides a better understanding of the tensions involved. Increasing investment in skilled non-college education will require addressing the concerns raised there.

So I thought I’d give it a shot. Here’s what I won’t take on:

  • Whether career/tech ed is worth it–This Post story shows that getting a certificate from community college only increases income by $1500/year, which is far better than getting the credential from a for-profit school, which loses people $900/year. Wait, what? For other minds than mine, though.
  • Business involvement—certainly, businesses will benefit and thus should fund part of this effort. I’m not sure how, though, and again, turn over to other minds.
  • Currency–how do you keep the offerings current? When does it make sense to put resources into training people for a new field? How are winners and losers declared?

All outside my ken. Designing these features hold no interest for me. Because if the system doesn’t address the disparate impact issue I discussed here, then it will ultimately fail either through lawsuit or lack of interest.

A couple years ago, I offered educational solutions, or at least options, for students of middle to low cognitive ability, in Just a Job. The programs I sketch out could easily be included in this program.

I envision “career” or “skills” training, as being designed for cognitive ability levels a bit above and a bit more below average. If using IQs, from 85 to 105.

Ban college-level remediation

Right now, we spend millions, at least, on students who are incapable of doing genuine college level work. We loan them money to take courses for which they will get no credit—loans which they will often be incapable of paying back. We spend money on instructors, on space, on curriculum. We deny increased opportunities to qualified students in the form of reduced schedules, thanks to the increased costs of remediation.

Increasing the opportunities for vocational/career training requires setting a standard for college access. We have to stop spending somewhere in order to pay for expanding vocational options. Freeing up the wasted money on wasted college spending is a good place to start. I lay out the case in the attached link.

Increasingly people push to do away with remedial education, which would mean colleges wouldn’t be forcing students to take remedial courses. Marc Tucker, for example, thinks it’s unfair that community colleges require their students to know any advanced math, since the jobs they’ll take on won’t need that math.

But if advanced math isn’t needed for the job, then why is the job requiring college? As I said at the end of the original essay: If no one is too incapable for college, then no education is remedial. So give the students credit for remedial courses, let barely functional students get college degrees after 120 credits of middle school work. No?

(OK, you have to be wondering if I’ve noticed that banning remediation is the Mother Of All Disparate Impact Lawsuits waiting to happen. I did. The rest of the proposal is designed to withstand all but the most illogical objections.)

Limit the scope of community college.

Most states offer three levels of vocational education: high school, community college and regional career centers. The last two are far more extensive than high school programs. Community colleges have appropriated many trade credentials (cosmetology, dental hygiene, auto-mechanics, etc). Low cost, but with often absurd waiting lists, community colleges attach many general education requirements to maintain the illusion of college and an AA degree.

That’s in addition to community college’s original mission: to provide an affordable method of taking general ed courses that will transfer to a four year college or provide stand alone associate degrees. Moreover, community colleges own the bulk of remedial education.

So in this new world, community colleges should be required to dump remedial education, which should be returned to adult education (more on that in a minute). Community colleges should only accept college ready students, as defined in the first step.

I can’t say conclusively that all career training should be removed from community college, which Wikipedia says handles 30% of all CTE. Some career training may have a significant academic requirement that warrant an associate’s degree. But if we are to develop meaningful non-college career training, it can’t be in college, which has a wide range of priorities and is also motivated to devote resources to immigrants.

Increase adult education funding.

Banning college remediation would be incredibly controversial. Many will correctly point out the disparate impact of this ban, that it’s funding higher education for predominantly white and Asian kids. What they wouldn’t mention is that restricting college for the qualified, regardless of race, would improve access and resources for the qualified low income students, again regardless of race.

However, everyone should have the opportunity to become college ready. Not everyone “gets it” the first time, and others finally decide to get serious about the brains they were given. All remediation, K-12 education that simply improves abilities or helps prepare for college, must be shifted to the adult education category, currently funded out of the K-12 budget but now (I hope) would have its own category.

Centralize training programs at the regional level

Someone’s going to ask why not private training programs. Go away and leave me be.

So community colleges should retain their original academic mission for college ready students. Adult education should include both adult remedial education institutions (which would be repurposed community colleges) and the regional career training centers. As I mentioned, many states offer these regional training centers already. These centers offer the best solution to skills education that crosses boundaries from high school to early college—and beyond, for those returning to the trades. All those in the area could attend their local center or apply for a center in another region, much like applying to local vs out of state public colleges today. Students can attend a combination of high school/college and regional trade school as needed.

Critically, students opt in to career training. If the students choose to enter the trades, high schools can’t be held responsible for sending them there. This reduces the potential for racism charges.

Increase resources, reduce selectivity

Today, thanks to the scarcity of career tech vocational programs, at least half the kids accepted are more than smart enough for college and would easily pass a placement test. But if step 1 is implemented, college is going to be much more challenging and college readiness will be a much bigger deal, particularly for those who can achieve it easily.

The “lower half” or more of the kids accepted to these selective programs are generally ambitious, hardworking dedicated kids who know they aren’t academic, but understand they need to have a good GPA. They stay focused. They work hard. They get internships. They get accepted into journeyman positions or move onto the next level of trade schools. They do this with the blessing and support, the letters, the advice, the guidance of their teachers and administration who—please know this—do not sneer at their career choices.

But if these rigorous, selective career and technical programs only accept the kids dedicated and focused enough to avoid all manner of screw-ups, the kids who schlep around, get suspended a few times, flunk math because they think the teacher’s a jerk, have shut themselves out of these options, often before they’re old enough to take advantage of them. Others start out motivated, then lose focus and can never get back on that path.

So “career-technical training”, voc-ed, or whatever you call it, is an excellent option for a lot of low-to-mid cognitive ability kids, but we have to recognize certain realities. These kids will be disproportionately, but not exclusively, black and Hispanic. These kids won’t always be perfectly motivated with spotless resumes.

Keep standards realistic, but challenging. Give kids a reason to work hard to qualify for a program that interests them. Then, be absolutely sure there are seats available for the qualified kids.

Qualify for skilled training using the ASVAB

Elites tend to think anyone not as smart as they are exist in a vast undifferentiated blob. Firefighter, plumber, truck driver, fast food worker–it’s all the same. But in fact, “the trades” encompasses a wide range of cognitive ability levels, and creating a fair means of ensuring rigor in the programs. The military’s ASVAB would be well-suited for this.

And–key plot point–students who need to work and study to qualify for a higher score can use the adult education program to get the support they need.

Build economies around the career centers

Remember, Brooks wants high schools to provide career and technical training so that their students can train and then leave the area. Given the expense of career tech, what states would willingly fund programs to train kids to leave the state?

But if the career centers themselves can rejuvenate–or at least bolster–a weak economy, it might not seem so pointless.

For example, West Virginia could place specialized regional centers in its ten poorest counties, each one focusing on a rigorous technology. Maybe not all–or even some–of the locals can qualify for the technology, but the center itself would provide jobs. The trainers and teachers relocated to the area would spur some growth as well.

Invest in the students

I don’t know if it makes more sense to subsidize career training through low-cost tuition or low-cost loans. Probably some of both. Certainly remedial education should be inexpensive and readily available (although we should not fund living expenses for remedial ed). Essential, though, is the understanding that the investment spigot isn’t shut off for kids who aren’t eligible for college. If, as I suggest, we close off college for many, the money saved must be spent not only on increasing resources for low-income college-ready students, but also on training and investment for students who won’t be going to college.

So there’s the broad outline.

Mentioned briefly here, but the main point of my tweet storm and Just a Job: restricting immigration is essential to invigorating the job and training market for the low skilled. (Note to Brooks: Rick Hess, AEI point man on education, pointedly observed a federal role for education that you might want to write about next time.) Until such time as we finally dramatically restrict immigration, we should at least limit our investment to citizens. Not just the loans, either. (To reiterate, I don’t hate immigrants. But they have no place in our educational system these days. Too expensive.)

We need to advance the debate on skills training, from say age 16 and older. We need to get beyond the tired tripe of “education needs to stop demonizing blue collar work” and start understanding why so few options exist. The only people glorifying college are the progressive and conservative elites. Us proles in the middle are just fine with jobs.

But if we are to start dealing with the difficult challenges that come with a diverse society with wide ranges in cognitive ability, motivation, and needs, then we need to stop the combination of “everyone can succeed” happy talk and “schools SUCK!” condemnation that consumes the discourse today.

Vocational Ed and the Elephant

I thought I’d expand my tweet storm on Arthur C. Brooks directive on American relocation, on one point at least. The one involving the Voldemort View, which must not be spoken. Here referred to as the elephant, because it scanned better.


Rod Dreher and his commenters go to this well all the time, about the so-called snobs who sneer at vocational education. Mike Rowe has built a career on it.

But these calls for a friendlier approach to vocational ed, aka CTE, aka career tech, completely misunderstand the reasons for its relative scarcity, which mostly have to do with the elephant in the room.

Keep in mind that the US has never experienced a halcyon period when committed, focused students were provided with meaningful careers through a helpful high school career training program. The term “dumping” has been around for a long time. A 1985 review of California’s vocational ed program showed that high school courses resulted in no improvement in employment or graduation rates, and even regional training centers had little impact on employment. The country’s support for any sort of vocational ed has always been tepid and cyclical. So it’s not as if we had a fantastic functioning vocational education system before the modern era.

The latest cycle began when 1983’s Nation at Risk forced radical changes in high school education in a failed attempt to raise standards. Nation badly damaged what successful vocational ed we had by arguing we needed rigorous preparation and high expectations to get more high school students ready for college. Of course, not everyone could meet the higher standards, because otherwise there’d be no point to the higher standards. The authors expected that students who weren’t ready for college would be well-trained by rigorous vocational education; they just didn’t think about the elephant.

See, Nation‘s call for high standards, joined five years later by Bill Bennett’s report update , dismissed any notion of an achievement gap. The achievement gap, according to these Ur-reformers, owed its origins not to poverty and ability, but unprepared teachers with low expectations and parents who didn’t care as much. Over time, education reformers stopped blaming parents.

But really, blame is irrelevant. Everything is irrelevant, there sits the elephant firmly in the center of unspoken space: large, cranky, completely ummovable. The kids who couldn’t, and still can’t, manage college prep curriculum are disproportionately black and Hispanic and, (often separately, alas) poor. So the insistence that “everyone could succeed”, with “succeed” meaning “go to college” led to that form of accountability otherwise known as lawsuits, which found that tracking resulted in disparate impact, which meant that tracking ended. Everyone took or tried to take college prep, and high school standards declined. Since everyone was taking college prep, no need for vocational ed, which became more of a dumping ground than usual. The low quality and already weak statistics eventually killed funding for the highest quality career training of the 80s and early 90s. (“Nation at Risk Killed Voc-Ed is mine own opinion, but this 2000 NCES report shares it, pg 49).

While many ambitious vocational ed programs were often killed in the Nation era, the next conservative reform movement, “No Child Left Behind”, resulted in an unexpected rebirth of excellence. Forced to prove themselves in order to avoid closure, the remaining voc-ed programs had to keep test scores high. So many career-oriented programs basically re-emerged as rigorous, but incredibly expensive and hard to staff. No longer a dumping ground, career-tech ed (CTE) supply is now outstripped by demand. The programs can pick and choose; the cognitive ability levels required are quite high. Today, career technical training is outstanding, demanding, and extremely selective. At least half the students strong enough for career training programs can easily place into college. The kids who can’t pass Algebra aren’t qualifying for career programs.

So “more technical training” in high school isn’t a magic bullet. Brooks’ AEI stable includes probably the best conservative reform policy guru, Rick Hess. If Brooks asked Rick about vocational education, the answer might have looked something like this:


Comparing Hess’s response to Brooks’, I’m figuring Hess wasn’t asked.

Or Brooks could have read up on Michael Petrilli’s push for moving more kids to career training. Petrilli, president of Fordham Foundation’s education reform think tank, published a harsh message for low ability kids in 2014: Sorry, Kid, You’re Just Not College Material, proposing that kids who can’t cut it in academic courses be rerouted into career and tech ed.

And Petrilli got schooled and schooled hard, as dozens of experts handed him his ass, explaining the history of vocational education, calling him a racist for writing off poor kids of color, pointing out the racial disparities, and basically calling him an uneducated yutz for blindly suggesting solutions that he didn’t understand. Anyone thinking of suggesting changes to vocational/career ed has no better starting point than Petrilli’s chagrined follow up acknowledging the error of his ways, and sounding a bit depressed about the cognitive demands of career training.

Yet here Brooks is, pushing career training again, ignoring the very recent experience of someone on his own team, blandly suggesting vocational education, continuing to avoid the Unspeakable. Twas ever thus. It’s always this vague notion that schools sneer at anything but college degrees, Brooks’ idee fixe. No one ever goes past this reason to wonder why high schools don’t track anymore.

I’m not sure anyone really understands why, until they have their noses shoved into it like Petrilli did. People just don’t understand the degree to which many high schools are forced to choose between failing most of their students year after year, with no hope of ever achieving three years of advanced math or English—that it’s not a matter of trying harder, or teaching better, or that the kids weren’t taught. They lack any real understanding of the layers of cognitive ability. They don’t realize there are perfectly normal folks who aren’t smart enough to be plumbers, welders, or dental hygienists.

But those who do understand often sound callous or dismissive of people with low IQs. Maybe it’s because my father cooks a great meal, fixes a great plane, and has a sub-100 IQ, or maybe it’s just because I was raised working class. Maybe it’s my work as a teacher. But I don’t think “low IQ” is an insult or a dismissal. And so, I’m angry at those who make basically ignorant proposals–move more! create more plumbers!–without even the slightest understanding of the political and social tensions that stop us from tracking kids by ability to the extent that, perhaps, we should.

I have never seen the cause of those tensions more eloquently expressed than in this panel on Education for Upward Mobility, by Howard Fuller. After an early life as a black activist (or maybe “after” is the wrong word), Fuller went on to become superintendent of Milwaukee Public Schools. Pro-charters, pro-choice, the embodiment of neo-progressive education reform and in every way imaginable a partner with Petrilli, the panel moderator, who asked him his thoughts on how best to shake off the ugly history of tracking and use it to help kids succeed. It’s best to listen to him say this, around minute 12, but for those who won’t bother, here’s what Fuller had to say:

“You know Mike, my thing, starting with the whole ‘who goes to high school'[think he means college]….most of the people who talk about ‘kids don’t need to go to college”, hell, they went to college. And so that’s where my problem starts right there. Why is it okay for you, but for these low income kids, “aw, y’all can’t go to college.” ….What do rich people do for their kids?….When I hear some of y’all talk about [vocational education], just know that I’m gonna always be suspicious. It brings up to me…somehow we’re trying to figure out a way…it’s almost like a Booker T./Du Bois argument brought up to this century. Whenever I hear the Booker T. part of that argument, it’s that we’re going to accept that a certain group of people are going to have to be in the lowest level, because that’s the way our economy is set up and so some of these kids, it’s okay for them to be there….And when people say tracking….the issue of power and whose kids get tracked in what ways and where they end up…I can’t get it out of my head…..I’m afraid of whose going to make what choices for what kids.”

This is what’s known as a facer. I have two simultaneous reactions. First, I’m impatient, because Fuller’s response just kills all rational conversation dead. There’s really no way past that. It’s brilliant, effective, and utterly deadening. Why here, I’ll just point out the elephant in the room, shall I? And because everyone’s busy pretending the elephant doesn’t exist, their scrotums will retract up into their livers. We’ll just change the subject, shall we?

But my second reaction, coming right afterwards, is doubt. Brooks’s op-ed is one of many sneering at the working class these days. The GOP head of Congress is wondering if he can talk Trump out of immigration restriction, since his own position is amnesty and more immigration for skilled workers , while Clinton wants amnesty and more immigration of every sort.

So I’m not entirely convinced anymore that Howard Fuller is entirely wrong to doubt the intentions of the elites who want so desperately to make decisions for all the little people.

But that won’t stop me from suggesting a system for career/tech training, of course. Stay tuned.

The Many Failings of Value-Added Modeling

Scott Alexander reviews the research on value-added models measuring teacher quality1. While Scott’s overview is perfectly fine, any such effort is akin to a circa 1692 overview of the research literature on alchemy. Quantifying teacher quality will, I believe, be understood in those terms soon enough.

High School VAM is Impossible

I have many objections to the whole notion of modeling what value a teacher adds, but top of the idiocy heap is how little attention is paid to the fact that VAM is only even possible with elementary school teachers. First, reading and basic math are the primary learning objectives of years 1-5. Second, elementary schools think of reading and math ability in terms of grade level. Finally, elementary teachers or their schools have considerable leeway in allocating instruction time by subject.

Now, go to high school (of which middle school is, as always, a pale imitation with similar issues). We don’t evaluate student reading skills by grade level, but rather “proficiency”. We don’t say “this 12th grader reads at the 10th grade level”. We have 12th graders who read at the 8th grade level, of course. We have 12th graders who read at the third grade level. But we don’t acknowledge this in our test scores, and so high school tests can’t measure reading progress. Which is good, because high school teachers aren’t tasked with reading instruction, so we wouldn’t expect students to make much progress. What’s that? Why don’t we teach reading instruction in high school, if kids can’t read at high school level, you ask? Because we aren’t allowed to. High school students with remedial level skills have to wait until college acknowledges their lack of skills.

And that’s reading, where at least we have a fighting shot of measuring progress, even though the tests don’t currently measure it–if we had yearly tests, which of course we don’t. Common Core ended yearly high school tests in most states. Math, it’s impossible because we pass most kids (regardless of ability) into the next class the next year, so there’s no “progress”, unless we measure kids at the beginning and end of the year, which introduces more tests and, of course, would show that the vast majority of students entering, say, algebra 2 don’t in fact understand algebra 1. Would the end of year tests measure whether or not the students had learned algebra 1, or algebra 2?

Nor can high school legally just allocate more time to reading and math instruction, although they can put low-scoring kids in double block instruction, which is a bad, bad thing.

Scope Creep

Most teachers at all levels don’t teach tested subjects and frankly, no one really cares about teacher quality and test scores in anything other than math or reading, but just pretend on everything else. Which leads to a question that proponents answer implicitly by picking one and ignoring the other: do we measure teacher quality to improve student outcomes or to spend government dollars effectively?

If the first, then what research do we have that art teachers, music teachers, gym teachers, or, god save us, special education teachers improve student outcomes? (answer: none.) If the second, then what evidence do we have that the additional cost of testing in all these additional topics, as well as the additional cost of defending the additional lawsuits that will inevitably arise as these teachers attack the tests as invalid, will be less strain on the government coffers than the cost of the purportedly inadequate teachers? What research do we have that any such tests on non-academic subjects are valid even as measures of knowledge, much less evidence of teacher validity?

None, of course. Which is why you see lawsuits by elective teachers pointing out it’s a tad unfair to be judged on the progress of students they’ve never actually met, much less taught. While many of those lawsuits get overturned as unfair but not constitutional, the idiocy of these efforts played no small part in the newest version of the federal ESEA, the ESSA, killed the student growth measure (SGM) requirement.

So while proponents might argue that math and English score growth have some relationship to teacher quality in those subjects, they can’t really argue for testing all subjects. Sure, people can pretend (a la Common Core) that history and science teachers have an impact on reading skills, but we have no mechanism to, and are years away from, changing instruction and testing in these topics to require reading content and measuring the impact of that specific instruction in that specific topic. And again, that’s just reading. Not math, where it’s easy enough to test students on their understanding of math in science and history, but very difficult to tangle out where that instruction came from. Of course, this is only an issue after elementary school. See point one.

Abandoning false gods

For the past 20 years or so, school policy has been about addressing “preparation”, which explains the obsession with elementary school. Originally, the push for school improvement began in high school. Few people realize or acknowledge these days that the Nation at Risk, that polemic seen as groundbreaking by education reformers but kind of, um, duh? by any regular people who take the time to read it, was entirely focused on high school, as can be ascertained by a simple perusal of its findings and recommendations. Stop coddling kids with easy classes, make them take college prep courses! That’s the ticket. It’s the easy courses, the low high school standards that cause the problem. Put all kids in harder classes. And so we did, with pretty disastrous results through the 80s. Many schools began tracking, but Jeannie Oakes and disparate impact lawsuits put an end to that.

I’m not sure when the obsession with elementary school began because I wasn’t paying close attention to ed policy during the 90s. But at some point in the early 90s, it began to register that putting low-skilled kids in advanced high school classes was perhaps not the best idea, leading to either fraud or a lot of failing grades, depending on school demographics. And so, it finally dawned on education reformers that many high school students weren’t “academically prepared” to manage the challenging courses that they had in mind. Thus the dialogue turned to preparing “underserved” students for high school. Enter KIPP and all the other “no excuses” charters which, as I’ve mentioned many times, focus almost entirely on elementary school students.

In the early days of KIPP, the scores seemed miraculous. People were bragging that KIPP completely closed the achievement gap back then, rather than the more measured “slight improvement controlling for race and SES” that you hear today. Ed reformers began pushing for all kids to be academically prepared, that is hey! Let’s make sure no child is left behind! And so the law, which led to an ever increasing push for earlier reading and math instruction, because hey, if we can just be sure that all kids are academically prepared for challenging work by high school, all our problems will be fixed.

Except, alas, they weren’t. I believe that the country is nearing the end of its faith in the false god of elementary school test scores, the belief that the achievement gap in high school is caused simply by not sufficiently challenging black and Hispanic kids in elementary school. Two decades of increasing elementary scores to the point that they appear to have topped out, with nary a budge in high school scores has given pause. Likewise, Rocketship, KIPP, and Success Academy have all faced questions about how their high-scoring students do in high school and college.

As I’ve said many times, high school is brutally hard compared to elementary school. The recent attempt to genuinely shove difficulty down earlier in the curriculum went over so well that the new federal law gave a whole bunch of education rights back to the states as an apology. Kidding. Kind of.

And so, back to VAM….Remember VAM? This is an essay about VAM. Well, all the objections I pointed out above–the problems with high school, the problems with specific subject teachers–were mostly waved away early on, because come on, folks, if we fix elementary school and improve instruction there, everything will fall into place! Miracles will happen. Cats will sleep with dogs. Just like the NCLB problem with 100% above average was waved away because hey, by them, the improvements will be sooooo wonderful that we won’t have to worry about the pesky statistical impossibilities.

I am not sure, but it seems likely that the fed’s relaxed attitude towards test scores has something to do with the abandonment of this false idol, which leads inevitably to the reluctant realization that perhaps The Nation At Risk was wrong, perhaps something else is involved with academic achievement besides simply plopping kids in the right classes. I offer in support the fact that Jerry Brown, governor of California, has remained almost entirely unscathed for shrugging off the achievement gap, saying hey, life’s a meritocracy. Who’s going to be a waiter if everyone’s “elevated” into some important job? Which makes me wonder if Jerry reads my blog.

So if teacher’s don’t make any difference and VAM is pointless, how come any yutz can’t become a teacher?

No one, ever, has argued that teachers don’t make any difference. What they do say is that individual teacher qualities make very little difference in student test scores and/or student academic outcomes, and the differences aren’t predictable or measurable.

If I may quote myself:

Teaching, like math, isn’t aspirin. It’s not medicine. It’s not a cure. It is an art enhanced by skills appropriate to the situation and medium, that will achieve all outcomes including success and failure based on complex interactions between the teachers and their audience. Treat it as a medicine, mandate a particular course of treatment, and hundreds of thousands of teachers will simply refuse to comply because it won’t cure the challenges and opportunities they face.

And like any art, teaching is not a profession that yields to market justice. Van Gogh died penniless. Bruces Dern and Davison are better actors than Chrisses Hemsworth and Evans, although their paychecks would never know it. Teaching, like art and acting, runs the range from velvet Elvis paint by numbers to Renoir, from Fast and Furious to Short Cuts. There are teaching superstars, and journeyman teachers, and the occasional lousy teacher who keeps working despite this–just as Rob Scheider still finds work, despite being so bad that Roger Ebert wrote a book about it.

Unlike art and acting, teaching is a government job. So while actors will get paid lots of money to pretend to be teachers, the job itself will never lead to the upside achieved by the private sector, despite the many stories about famous Korean tutors. Upside, practicing our craft won’t usually lead to poverty, except perhaps in North Carolina.

Most teachers understand this. It’s the outside world and the occasional short-termers who want teachers to be rewarded for excellence. Most teachers don’t support merit pay and vehemently oppose “student growth measures”.

The country appears to be moving towards a teacher shortage. I anticipate all talk of VAM to vanish. But if you want to improve teacher quality beyond its current much-better-than-it’s-credited condition, I suggest we consider limiting the scope of public education. Four of these five education policy proposals will do just that.

1 I was writing this up in the comments section of Scott Alexander’s commentary on teacher VAM research, when I remembered I was behind on my post quota. What the heck. I’m turning this into a post. It’s a long answer, but not as long-winded as Scott Alexander, the one blogger who makes me feel brusque.

Great Moments in Teaching: The Third Dimension (part I)

“How many other dimensions are there?”

“Well, four, according to Einstein, and five according to Madeline L’Engle, if you’ve read A Wrinkle in Time.”

“I have!” Priya’s hand shot up. “It’s a tesseract!”

I was impressed. Not many girls read that classic anymore. “But we’re going to stick to three dimensions.”

“Isn’t real life three dimensions?” asked Tess.

“Yes. But if you think of it, up to now, we’ve only been working in two. We’ve spent a lot of time in the coordinate plane thinking about lines. In two dimensions, a line can be formed by any two points on the coordinate plane. We’ve been working with systems of equations, which you think of as algebraic representations of the intersections of two lines. We can also define distance in the coordinate plane, using the Pythagorean theorem. All in two dimensions.”

Now, no mocking my terrible art skills” and I put up this sketch, the drawing of which occurred to me the night before, and was the impetus for the lesson.


Everyone gasped, as they had in the previous two classes. My instincts about that clunky little sketch proved out, beautifully. No clue why.

“Holy sh**,” groaned Dwayne, the good ol’ country boy who offered to paint my ancient Honda if I gave him a passing grade. He doesn’t like math. He’s loud and foul and annoying and never shuts up. That last sentence is a pretty good description of me, so I’m very fond of him. “What the hell is that? Get it off the screen, it hurts my eyes.”

“That is awesome,” offered Talika, a senior I had last year for history. “How long did it take you to draw that?”

“What is that white stuff spread everywhere? Did someone get all excited?” asked Dylan, a sophomore whose mother once emailed me about his grade, giving me the pleasure of embarrassing him greatly by describing his behavior.

“Ask your mother,” I replied, to a gratifying “ooooo, BURN!” from the class, who knew very well what had happened.

“How did you draw that?” asked Teddy, curious. “It’s not ordinary graph paper, right?”

“No, it’s isometric paper, which allows you to draw three dimensional images. So…”

“This is really stupid,” said Dwayne. “I’ve taken algebra 2 three times and no one’s ever taught me this.”

“Best I can tell, no one’s ever taught you anything , and not just not in algebra 2,” I replied, earning another “Oooooo” from the class and an appreciative chuckle from Dwayne.

“It’s weird, though, because in two dimensions, you start in the middle,” offered Manual, who was consulting with Prabh, another bright kid who rarely speaks.

“That’s a good point! For example, if we were going to plot seating positions in this room in two dimensions, we’d start with Tanya,” I said, moving to the class center and indicating Tanya, who looked a bit confused. “So Tanya would be the origin, and Wendell would be (1,0), while Dylan would be (1,-1).”

“I’m not negative!” Dylan said instantly, talking over my attempt to continue. “You’re saying I’m negative. You don’t like me.”

“Hard to blame anyone for that,” said Wendell who is considerably more, er, urban than Teddy, with pants down to his knees and a pick that spends some time in his hair. Despite his occasional class naps, he maintains a solid C+, and could effortlessly manage a B if I could just keep him awake. “S’easy, dude. It’s like one of those x y things, like we’re all dots on the graph.”

“You’re one down and one to the right of me,” pointed out Tanya.

Dylan was interested in spite of himself. “So Talika’s, like, (0, 4)?”

“Yes,” several students chorused.

“Then I’m negative 8.” said Dwayne, unhappy with any conversation that doesn’t have him at the center.

“More like….(-2,2), yeah,” says Cal.

Ben speaks up, “But how come Tanya’s at the center for mapping the room’s people, but your sketch is, like, from the left?”

“Or right?” Sophie, from the back.

“Or is it….outside?” asks Manuel.

“Yes, it’s kind of like you’re standing on a desk in Ms. Chan’s room and the walls are transparent,” says Ben, more certainly. Ben is repeating Algebra 2 after having taken it with me last semester. Very bright kid who clowned incessantly, confident in his ability to learn without really trying, only to learn that Algebra 2 was different from other nights, and he wasn’t finding the afikoman. I advised him to repeat. The big sophomore not only agreed, but specifically asked to repeat with me. His attitude and behavior is much improved. I ran into him while walking across the courtyard a few weeks earlier, and he said “I just realized I was Dwayne and Dylan combined last semester, and it’s so embarrassing. I’m really sorry.”

“I’m not enough of an artist to know if I could have drawn this any other way. It just seemed intuitive to me last night, when I came up with the idea.”

“See, I knew it,” trumpeted Dwayne. “You’re making this up!”

“Yeah, I know this isn’t in any algebra book” said Wendy, a sophomore whose excellence in math is often hard to discern beneath her complaints. “This is just some weird thing you’re doing to make us think about math.”

I picked up at random one of the four algebra 2 books sitting on my desk (I’m on the textbook committee) and walked over to Wendy’s desk, opening it to the “Three Dimensional Systems” chapter. She looked, and said “Ok, maybe not.”

“So just as we can plot points in two dimensions, we can plot points in three. Take Aditya here,” my TA, who was watching the circus in amusement. “How could we represent him as a point on my graph?”

Teddy said instantly, “Yeah, I’ve been working that out. I can’t figure out which the new one is, and what do we call it? Where’s x, where’s y?”

Sanjaya said, “I think the part along the ground is x. Like if you go along the bookshelf?”

“Like this?”


“Yes,” Sanjaya said, confidently. “That has to be x. So you could count to Aditya, right?”

“Count which way?”

“The bottom!” “The bottom line!” “the bottom..axis, thing. The X!” comes a chorus of voices.

I start counting, and while I do, Sophie objected. “But hang on. I still don’t see what the new thing, direction, is. What’s the third?”

“Up! said Calvin, who rarely participates and often tunes out so far he can’t keep up. But he was watching this with interest. “You know how the class map with Tanya was going north and south and east and west. But it’s all flat, like. This picture has an up.”

“Yeah!” Ben got it. “Cal’s right.”

Dwayne has begun to grasp this. “So you can’t just draw a line? You have to follow along the…things?”

“The axes.” I finish counting along the “bottom” axis and go over to my bookshelf in the furthest corner of my room. “So the sketch starts here…QUIET! One conversation at a time, and I’m the STAR here. The origin starts at this bookshelf. I am walking along the wall, hugging it, on my way to Aditya. Does everyone see how they could track my progress on the axis?”

“YES!” from various points of the room.

“What the hell are you doing?” Dwayne is watching me carefully hug the wall.

“Everyone except Dwayne?”

“YES!” much louder.

I walked along the wall to the table where Aditya sat (fourth along the wall) and stop.

“So now what?”

“You’re there.”

“No, not yet.” countered Nadine. You have to go out….” she waved me towards her. “this way.”

“Yeah, towards Aditya,” this from Talika.

I stepped out 2 steps or so. “That all?”

Josh frowned. “Yeah. You’re there. Except…”

“UP!” Sophie shouted from the back. “That’s the third axis!” General approval reigns loudly, until I wave them all quiet, or try to.

“You go up 4!” Teddy shouted.

“OK. So Aditya is about 40 units out along the wall, 2 units out towards…the door, and 4 units up. Yes?”


“So let’s draw that.”

Of course, while I’m drew this, general mayhem is ongoing with my back turned. I shouted “QUIET! or “Could someone stick a sock in Dwayne?” a few times.

“Wow, so it’s a…cube?”

“A prism, yes. So here’s what we’ve done. We’ve taken the two dimensional x-y coordinate plane and extended it.”

“We extended it up,” from Sophie.

“Yes. And now, instead of a rectangle, we have a three-dimensional rectangular prism. And we can describe things now in three dimensions. But we can do more than that. So let’s step away from my classroom sketch….”


“Whoa. What’s that?” Dylan.

“Man, that’s f***ed up. I just started to get this, and now you’re….” Dwayne, of course.

“No, it’s fine,” Manuel said. “It’s just like the whole thing moved to the center.”

“Oh, I see. It’s like there’s four rooms, all cornered.” Wendell.

“Yes, exactly. Except now, you want to stop thinking about it as a room and think of it as a coordinate plane. As Sophie says, the new plane is the up/down one. So the old x is now here. The old y is now here. The z is the straight up and down one. I think of it as taking the 2 dimensional plane and kind of stepping back and looking down on it.”

“That’s just….”

“DWAYNE BE QUIET. One thing to remember: when you see a 3-dimensional plane, they may be ordered differently. There’s a whole bunch of rules about it that make potentially obscene finger orientations, but I promise I won’t test you on that.”

“So let’s say we’re plotting the point (8,4,5). I’m going to show you how to do it first. Then I’ll go through why. Start by plotting the intercept along each of the planes.”

“Man, does anyone else get this?”

“YES. Shut up, Dylan,” says Natasha.


“The trick to remember when you’re graphing in 3-d is to stay parallel to the axis you’re drawing along. So never cross over the lines when plotting points. Now let’s add the yz and xz planes.

“What? This is weird. Why are you drawing so many rectangles?” Patty, frowning.


“What you have to visualize is that it’s like we’re drawing sides. So far, I’ve drawn,” I look around and grab three of my small whiteboards, “the bottom and two of the sides. Hold this, Natasha, Talika.” and I build the walls. The kids in the back stand up and look over.

“Oh, I see,” Teddy again. “You’re drawing the prism again.”

“Right. It’s just looking different because the axis is in the center.”

“You do all this just to plot one point?” Sophie, ever the skeptic.

“Yes, but remember this is more just to illustrate, to see how you can extend the dimensions. So after you draw the three sides, joining the intercepts for xy, yz, and xz intersections, you extend those out–again, along the lines.”


“So the point we’re graphing is going to be at the vertex, the intersection of the three planes, the furthest point from the origin–just like in two dimensions, the point is at the intersection of the two lines.”

“That’s really complicated.” Wendy sighed.

“No, it’s not” “Don’t you see the…” Ben, Manuel, Teddy, Wendell and others jump in at the same time, while Dwayne bellowed, Wendy and Tess were asking questions of the room, and, as the writer says, pandemonium ensued. It was a shouting match, yes, but they were shouting about math. The Naysayers, the Doubters, and the Apostles were all marking their territory and this was no genteel, elegant, “turn and discuss this with your partner”, no think-pair-share nonsense. This was a scrum, a brawl, a melee conducted across the room with the volume up at 11—but just like any good fight, there was order beneath the chaos, a give and a take at the group level.

And for you gentle souls wondering about the quiet kids, the introverts, the shy ones who need time to think, they were enthralled, watching the game and making up their mind. It may not look like everyone gets time to talk, but pretty much every time you read me call on a kid, it’s a quiet one. And I shush the room. Then the quiet kid sits there in shock as he or she realizes oh god, I’ve got the mike and I can’t be a spectator anymore.

Anyway, the story goes on with a second great moment, but I’m getting better at chunking and this half had too many details I didn’t want to give up. I’ll stop here for dramatic effect. Because oh, lord, I was high as a kite in this moment, watching the room, realizing I was riding a tremendous wave of energy and excitement. Yeah. ME. On Stage. Making Drama.1

Now I just had to come up with a good ending.

1I’m not congratulating myself, saying I’m proving kids with the great moment. No, the great moment is mine. I’m standing there going oh, my god, this is a great moment in teaching, in my life. For me! The kids, hey, if they liked it, that’s good.